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Statistics of Hecke eigenvalues for GL(𝑛)

  • Yuk-Kam Lau , Ming Ho Ng und Yingnan Wang EMAIL logo
Veröffentlicht/Copyright: 10. September 2018

Abstract

A two-dimensional central limit theorem for the eigenvalues of GLⁱ(n) Hecke–Maass cusp forms is newly derived. The covariance matrix is diagonal and hence verifies the statistical independence between the real and imaginary parts of the eigenvalues. We also prove a central limit theorem for the number of weighted eigenvalues in a compact region of the complex plane, and evaluate some moments of eigenvalues for the Hecke operator Tp which reveal interesting interferences.

MSC 2010: 11F12

Communicated by Jan Bruinier


Award Identifier / Grant number: 17302514

Award Identifier / Grant number: 17305617

Award Identifier / Grant number: 11501376

Award Identifier / Grant number: 2015A030310241

Funding statement: Lau is supported by GRF (Project No. 17302514 and 17305617) of the Research Grants Council of Hong Kong. Wang is supported by the National Natural Science Foundation of China (Grant No. 11501376), Guangdong Province Natural Science Foundation (Grant No. 2015A030310241) and Natural Science Foundation of Shenzhen University (Grant No. 201541).

Acknowledgements

The authors would like to thank Prof. Zeev Rudnick for valuable comments and Dr. Guangyue Han for helpful discussions.

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Received: 2018-07-13
Published Online: 2018-09-10
Published in Print: 2019-01-01

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